NUT charge weak gravity conjecture from dimensional reduction

We investigate the behavior of the Weak Gravity Conjecture (WGC) under toroidal compactification and RG flows, finding evidence that WGC bounds for single photons become weaker in the infrared. By contrast, we find that a photon satisfying the WGC will not necessarily satisfy it after toroidal compactification when black holes charged under the Kaluza-Klein photons are considered. Doing so either requires an infinite number of states of different charges to satisfy the WGC in the original theory or a restriction on allowed compactification radii. These subtleties suggest that if the Weak Gravity Conjecture is true, we must seek a stronger form of the conjecture that is robust under compactification. We propose a “Lattice Weak Gravity Conjecture” that meets this requirement: a superextremal particle should exist for every charge in the charge lattice. The perturbative heterotic string satisfies this conjecture. We also use compactification to explore the extent to which the WGC applies to axions. We argue that gravitational instanton solutions in theories of axions coupled to dilaton-like fields are analogous to extremal black holes, motivating a WGC for axions. This is further supported by a match between the instanton action and that of wrapped black branes in a higher-dimensional UV completion.

A bstract We point out that the Weak Gravity Conjecture (WGC) implies that sufficiently small extremal black holes are necessarily in the strong-field regime of electrodynamics, and therefore probe the UV completion of the Maxwell sector. To investigate the WGC bounds arising from these small extremal black holes, we revisit black hole decay in generic field theories in asymptotically flat space. We derive a necessary and a sufficient condition for any black hole to decay, the latter amounting to a bound on the growth of charge relative to mass. We apply these conditions to extremal black holes derived in various UV completions of the Maxwell sector. We find that the Euler-Heisenberg and DBI effective actions satisfy the sufficient condition for decay, while the ModMax model fails the necessary one, rendering it incompatible with the WGC. Using the decay conditions, we show that the black hole WGC implies positivity of the U(1) gauge coupling beta function. This provides an independent argument that classically stable (embedded-Abelian) colored black holes cannot exist. We also show that the black hole WGC constrains conformal hidden sector models, and is always satisfied in their AdS dual realizations.

We search for a possible relationship between weak gravity conjecture (WGC) and conformal field theory (CFT) in hyperscaling violating and Kerr-Newman-AdS black holes. We deal with the critical points of the black hole systems using the correlation function introduced in CFT and discuss WGC conditions using the imaginary part of the energy obtained from the critical points and their poles. Under the assumptions , , and , we link WGC to hyperscaling violating black holes owing to the existence of values larger and smaller than one. For the second black hole system, we study the conditions of WGC for Kerr-Newman-AdS black holes using rotation and radius parameters. Then, we show that the conditions of WGC are satisfied when the charged particle near the hyperscaling violating and Kerr-Newman black holes is with a ratio .

A bstract We investigate the constraints imposed by the Weak Gravity Conjecture (WGC) on gravitational lensing in gravity’s rainbow, focusing in particular on scenarios beyond extremality and on the interplay between the WGC and the Weak Cosmic Censorship Conjecture (WCCC) in the context of Reissner-Nordström-Anti-de Sitter black holes modified by rainbow gravity. Using topological methods, we first analyze the configuration of photon spheres and confirm that unstable circular photon spheres with topological charge ( ω = −1) exist outside the event horizon throughout the parameter space, thereby verifying the simultaneous validity of both the WGC and the WCCC. The rainbow functions f ( ε ) and g ( ε ), which encode Planck-scale corrections through the energy ratio ( ε = E/E P ), modify both the spacetime metric and the extremality bound. We derive the corresponding modified extremal charge-to-mass ratio, ( q 2 /m 2 ) > ( Q 2 /M 2 ) ext , and show that gravity’s rainbow offers a natural mechanism for reconciling these two fundamental conjectures. By applying the Gauss-Bonnet theorem in conjunction with Jacobi-Maupertuis optical geometry, we compute the weak deflection angles for both photons and massive particles to second order. The rainbow function g ( ε ) appears with powers ( g − 2 ) and ( g − 4 ), enhancing the deflection angle when g ( ε ) < 1, while f ( ε ) influences only the charge-dependent contributions. At extremality, the deflection angle becomes independent of f ( ε ), yielding a universal prediction that can be tested without specifying the form of the rainbow functions. We further find that super-extremal configurations exhibit stronger lensing effects than extremal black holes, suggesting a potential observational discriminator between WGC-satisfying naked singularities and WCCC-preserving black holes. These findings position gravitational lensing as a promising tool for probing quantum-gravity phenomenology with upcoming observational facilities.

It seems that the regime of Hawking radiation and evaporation ultimately drives charged black holes toward super-extremality of the charge parameter and the dominance of extremal conditions. This progression, in turn, lays the groundwork for satisfying the necessary conditions for the Weak Gravity Conjecture (WGC). Preliminary studies indicate that black holes such as the Reissner–Nordström (RN) model, in their initial form, lack the capacity to sustain super-extremality of the charge parameter. If such conditions arise, these black holes transition into naked singularities – a scenario that is highly undesirable due to the loss of causality and the breakdown of space–time geometry. This raises whether the inability to sustain super-extremality is an inherent property of the model or a consequence of the approximations and precision limitations employed in its construction. To address this, we turned to the ModMax model, which represents an extension of the RN model. Our analysis revealed that the ModMax model not only accommodates super-extremality of the charge parameter but also, under certain conditions, emerges as a promising candidate for investigating the WGC. Furthermore, we independently observed how the inclusion of the de Sitter radius ( $$\ell $$ ℓ ) in the AdS model and F(R) gravitational corrections – both of which enhance and complicate the model – can have a direct impact on the range of super-extremal charge tolerance which, in turn, provides the realization of the conditions necessary for the WGC.

In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particle’s mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that ‘gravity is the weakest force’. Here, we take a step towards making this expectation more precise by studying ℤN and ℤ2N gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to MPl.

We revisit the complexity = action proposal for charged black holes. We investigate the complexity for a dyonic black hole, and we find the surprising feature that the late-time growth is sensitive to the ratio between electric and magnetic charges. In particular, the late-time growth rate vanishes when the black hole carries only a magnetic charge. If the dyonic black hole is perturbed by a light shock wave, a similar feature appears for the switchback effect, e.g. it is absent for purely magnetic black holes. We then show how the inclusion of a surface term to the action can put the electric and magnetic charges on an equal footing, or more generally change the value of the late-time growt rate. Next, we investigate how the causal structure influences the late-time growth with and without the surface term for charged black holes in a family of Einstein-Maxwell-Dilaton theories. Finally, we connect the previous discussion to the complexity=action proposal for the two-dimensional Jackiw-Teitelboim theory. Since the two-dimensional theory is obtained by a dimensional reduction from Einstein-Maxwell theory in higher dimensions in a near-extremal and near-horizon limit, the choices of parent action and parent background solution determine the behaviour of holographic complexity in two dimensions.

Motivated by the Weak Gravity Conjecture, we uncover an intricate interplay between black holes, BPS particle counting, and Calabi‐Yau geometry in five dimensions. In particular, we point out that extremal BPS black holes exist only in certain directions in the charge lattice, and we argue that these directions fill out a cone that is dual to the cone of effective divisors of the Calabi‐Yau threefold. The tower and sublattice versions of the Weak Gravity Conjecture require an infinite tower of BPS particles in these directions, and therefore imply purely geometric conjectures requiring the existence of infinite towers of holomorphic curves in every direction within the dual of the cone of effective divisors. We verify these geometric conjectures in a number of examples by computing Gopakumar‐Vafa invariants.

Positivity bounds coming from consistency of UV scattering amplitudes are not always sufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved SL(2, ℝ) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved O(d, d; ℝ) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states.

We present a general method of computing corrections to the extremality bound and entropy of Kerr-Newman black holes due to an arbitrary perturbation using the Iyer-Wald formalism. In this method, corrections to the extremality bound are given by an integral over an effective stress tensor which, in particular cases of interest, reduces to the usual stress tensor. This clarifies the relation between extremality corrections and energy conditions. In particular, we show that a necessary condition to decrease the mass of an extremal black hole in a canonical ensemble, as required by the weak gravity conjecture, is that the perturbation violates the dominant energy condition. As an application of our method, we compute higher-derivative corrections to charged black holes in anti–de Sitter and Kerr black holes.

The Weak Gravity Conjecture (WGC) demands the existence of superextremal particles in any consistent quantum theory of gravity. The standard lore is that these particles are introduced to ensure that extremal black holes are either unstable or marginally stable, but it is not clear what is wrong if this doesn’t happen. This note shows that, for a generic Einstein quantum theory of gravity in AdS, exactly stability of extremal black branes is in tension with rigorously proven quantum information theorems about entanglement entropy. Avoiding the contradiction leads to a nonperturbative version of the WGC, which reduces to the usual statement at weak coupling. The argument is general, and it does not rely on either supersymmetry or a particular UV completion, assuming only the validity of Einsteinian gravity, effective field theory, and holography. The pathology is related to the development of an infinite throat in the near-horizon region of the extremal solutions, which suggests a connection to the ER=EPR proposal.

We observe that racetrack models for moduli stabilization are in tension with strong forms of the Weak Gravity Conjecture (WGC). Moreover, recently, it was noted that controlled KKLT-type de Sitter vacua seem to require a racetrack fine-tuning of the type introduced by Kallosh and Linde. We combine these observations and conclude that the quests for realizing parametrically large axion decay constants and controlled de Sitter vacua are intimately related. Finally, we discuss possible approaches to curing the conflict between the racetrack scheme and the WGC.

We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordström black holes for general dimensions and horizon geometries. We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution. In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that c − a is positive in the dual CFT. We discuss implications for the deviation of η/s from its universal value and a potential lower bound.

Constructing an explicit compactification yielding a metastable de Sitter (dS) vacuum in a UV consistent string theory is an incredibly difficult open problem. Motivated by this issue, as well as the conjecture that all non-supersymmetric AdS vacua must decay, we discuss the alternative possibility of realizing an effective four-dimensional dS cosmology on a codimension-one bubble wall separating two AdS5 vacua. The construction further elaborates on the scenario of arXiv:1807.01570, where the aforementioned cosmology arises due to a non-perturbative decay and is embedded in a five-dimensional bulk in a time­ dependent way. In this paper we discuss the relation between this scenario and the weak gravity conjecture and further develop the details of the four-dimensional cosmology. We provide a bulk interpretation for the dS temperature as the Unruh temperature experienced by an accelerated observer riding the bubble. A source of four-dimensional matter arises from a string cloud in the bulk, and we examine the consequences for the particle mass spectrum. Furthermore, we show how effective four-dimensional Einstein gravity on the bubble is obtained from the five-dimensional Gauss equation. We conclude by outlining some implications that this paradigm will have for holography, inflation, the standard model, and black holes.

We study (near-)circular orbits of charged particles in the background of charged black holes in asymptotically anti–de Sitter (AdS) spacetimes of arbitrary dimensionality. We calculate the energy and angular momentum of such particles in a large-radius limit. This allows us to compute the anomalous dimension of the dual charged double-twist operators in a large-spin expansion, making a prediction for the bootstrap analysis at large charge and spin. We relate our result to the weak gravity conjecture (WGC) for AdS black holes of all sizes. We also discuss the relation of WGC with the existence of the innermost stable circular orbit (ISCO) in any dimension. Published by the American Physical Society 2024